Hw9 - SIEO 3600(IEOR Majors Introduction to Probability and...

SIEO 3600 (IEOR Majors) Assignment #9 Introduction to Probability and Statistics March 30, 2010 Assignment #9 – due April 6th, 2010 ( Uniform, Exponential and Normal random variables ) 1. If X is a normal random variable with parameters μ = 10, σ 2 = 26, compute (a) P ( X > 5); (b) P (4 < X < 16); (c) P ( X < 8); (d) P ( X < 20); (e) P ( X > 16). Hint: express these probabilities in terms of the standard normal CDF function Φ and use the tables at the back of the textbook. 2. The annual rainfall (in inches) in a certain region is normally distributed with μ = 40, σ = 4. What is the probability that in 2 of the next 4 years the rainfall will exceed 50 inches? Assume that the rainfalls in diﬀerent years are independent. 3. A random variable X is said to have a lognormal distribution if Z ≡ log X is normally distributed. If X is lognormal with E [ Z ] = μ and var( Z ) = σ 2 , then (a) determine the probability distribution function (PDF) of X . (b) What is P ( X ≤ x )? 4. In the midterm of a probability course, the scores that students get follow a uniform distri-bution from 20 to 100. Due to popular grieving, the professor decides to rescale the results.

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